Download Finding trig ratios in right triangles

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Subject: Trigonometry 
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 Finding trig ratios in right triangles
The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric
ratios are the sine (sin), cosine (cos), and tangent (tan). These are defined for acute angle A below.
A
adjacent
opposite
hy
po
te
nu
se
B
C
sin(A) =
opposite
hypotenuse
cos(A) =
adjacent
hypotenuse
tan(A) =
opposite
adjacent
In these definitions, the terms opposite, adjacent, and hypotenuse refer to the lengths of the sides.
SOH-CAH-TOA: An easy way to remember trig ratios
The word sohcahtoa helps us remember the definitions of sine, cosine, and tangent. Here's how it works:
Acronym Part
Verbal Description
Mathematical Definition
SOH
Sine is Opposite over Hypotenuse
sin(A) =
CAH
Cosine is Adjacent over Hypotenuse
T OA
Tangent is Opposite over Adjacent
Opposite
Hypotenuse
Adjacent
cos(A) =
Hypotenuse
Opposite
tan(A) =
Adjacent
For example, if we want to recall the definition of the sine, we reference SOH , since sine starts with the
letter S. The O and the H help us to remember that sine is opposite over hypotenuse!
Let's study an example
Suppose we wanted to find sin(A) in △ABC given below.
A
5
4
C
B
3
Solution
Sine is defined as the ratio of the opposite to the hypotenuse (SOH). Therefore:
A
5
4
C
3
B
opposite sin(A) =
hypotenuse
BC
=
AB
=
3
5
[I'd like to see another example.]
Now let's try some practice problems